According to this page, Chaza"l intentionally omitted solar and lunar eclipses from the list of natural phenomena upon which we make a bracha. The following explanation is given:
"The Hebrew term for eclipse [is] LIKUI - defect. The Talmud states that a Likui of the Sun is a bad sign for the world; a lunar likui is a bad sign for Israel. Being associated with bad signs, the eclipse was not assigned a bracha. [...] During an eclipse, we witness the powerful, constant light and energy of the Sun being diminished. Or the light of a full Moon paling to a feeble glow. In both cases, we can read the chilling reminder that it is in G-d's Hands as to whether we live in light or suffer in darkness."
However, brachot are still made on earthquakes, thunderstorms, and winds strong enough to shatter stones and mountains. Surely these events are also chilling reminders that it is in G-d's Hands as to whether we live, suffer, or die. They threaten our individual, if not our collective existence, in a much more concrete way than any eclipse. Surely that much was known even in the time of our Sages.
So why make a bracha on these dangerous events, but not on an eclipse? Is the essential difference that the eclipse threatens our existence as a human race, whereas the others only threaten us as individuals? What of the fact that it is actually G-d, not the sun, Who gives us life?
EXTRA CREDIT: Why make a bracha on a rainbow but not on an eclipse? Rainbows are also considered a "bad omen," and yet we make a bracha on them. In 'light' of that fact, why don't we also make a bracha on an eclipse? Does it just come down to "Because Chaza"l said so?" (Thanks to Double AA for pointing out this aspect.)